Three stars A,B,C have surface temperature `T_A, T _B, T_C` resp. Star A appears bluish star B appears reddish and star C yellowish . Hence

Options

A. `T_A gt T_B gt T_C`
B. `T_B gt T_C gt T_A`
C. `T_C gt T_B gt T_A`
D. `T_A gt T_C gt T_B`

Answer

To solve the problem regarding the temperatures of the stars A, B, and C based on their colors, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Color and Temperature**:
- The color of a star is related to its surface temperature. Stars emit light of different colors depending on their temperatures.

2. **Identify the Colors and Their Corresponding Wavelengths**:
- Star A appears bluish, which corresponds to shorter wavelengths (higher energy).
- Star B appears reddish, which corresponds to longer wavelengths (lower energy).
- Star C appears yellowish, which corresponds to intermediate wavelengths.

3. **Order the Wavelengths**:
- Based on the colors:
- Wavelength of Star B (red) > Wavelength of Star C (yellow) > Wavelength of Star A (blue).
- This can be expressed as:
\[ \lambda_B > \lambda_C > \lambda_A \]

4. **Use the Inverse Relationship Between Wavelength and Temperature**:
- The temperature of a star is inversely proportional to its wavelength. This means:
\[ T \propto \frac{1}{\lambda} \]
- Therefore, if the wavelength is longer, the temperature is lower.

5. **Determine the Order of Temperatures**:
- Since Star B has the longest wavelength, it has the lowest temperature.
- Star C has an intermediate wavelength, so it has a higher temperature than Star B but lower than Star A.
- Star A, with the shortest wavelength, has the highest temperature.
- This leads to the following order of temperatures:
\[ T_A > T_C > T_B \]

6. **Final Conclusion**:
- The order of temperatures from highest to lowest is:
\[ T_A > T_C > T_B \]